Sylvie finds the solution to the system of equations by graphing. y = 2/3 x + 1 and y = -2/3x – 1 which graph shows the solution to sylvie’s system of equations?

Remark

One of the ways you could solve this is to go to a place like Desmos and graph it for yourself. Then at least you would know what the answer looked like. Another way is to solve for the x value by equating the equations since the y has to be the same. We'll do both.

Solve For X

(2/3)x + 1 = -(2/3)x - 1    Add 1 to both sides

(2/3)x + 1 + 1 = - 2/3x    Subtract (2/3x) from both sides.

2 = (-2/3)x - (2/3)x

Show the graph and comment

Notice that there is only one graph given that has a value of x = - 3/2 Normally you are not that lucky. Thanks for putting the graphs in. We are usually not that lucky and have to guess at the answer if it is a graph.

2 = - 4/3x                      Multiply both sides by 3

2 * 3 = - 4x    

6 = - 4x                          Divide by - 4

6/-4  = x                        Reduce

-3/2  = x

Remark

The x value is wrong for the one on the left.  It is also wrong for the third one from the left.  And the last graph is also incorrect.     Only the second from the left gives the right answer.                                      

1/800 is the right answer

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584